While it certainly is possible to start a blog for nothing by using free service like Blogger.com or Wordpress.com. I recommend every blogger starting to get their own domain name. The cost is next to nothing and you can still host it for free if you want (Blogger allows that). If you do not wish to use the Blogger platform, you’ll have to pony up for web hosting but that’s pretty damn cheap as well.
Having your own domain makes you look more professional. While it may not make you a pro-blogger, he ad networks will take you a lot more seriously. Some ad networks will not accept a site unless it has its own domain name. If you do it right, having your own domain and web hosing won’t cost you anything because the income the blog generates will more than offset the cost.

It’s better to get the domain name at the start than down the road. The last thing you want to do is build up a blog with Blogspot, get a ton of backlinks, PageRank, Alexa and Technorati rankings, and then have to move it to its own domain and start over.